Teacher s Guide - Activity P51: LR Circuit (Power Output, Voltage Sensor) Concept DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) Circuits P51 LR Circuit.DS (See end of activity) (See end of activity) Equipment Needed Qty From AC/DC Electronics Lab* Qty Voltage Sensor (CI-6503) 1 Inductor Coil and Iron Core 1 LCR Meter (SB-9754) 1 Resistor, 10 ohm 1 Multimeter (SE-9786) 1 Wire Lead, 5 inch (13 cm) 2 Patch Cords (SE-9750) 2 (*The AC/DC Electronics Lab is PASCO Model EM-8656) What Do You Think? What is the relationship between the voltage across the inductor and the voltage across the resistor in an inductor-resistor circuit? What is the relationship between the current through the inductor and the behavior of an inductor in a DC circuit? Take time to answer the What Do You Think? question(s) in the Lab Report section. Background When a DC voltage is applied to an inductor and a resistor in series a steady current will be established: V I o max R where V o is the applied voltage and R is the total resistance in the circuit. R L But it takes time to establish this steady-state current because the inductor creates a back-emf in response to the rise in current. The current will rise exponentially: ( R L ) t t / τ I = I ( 1 e ) = I ( 1 e ) max where L is the inductance and the quantity L R = τ is the inductive time constant. The inductive time constant is a measure of how long it takes the current to be established. One inductive time constant is the time it takes for the current to rise to 63% of its maximum value (or fall to 37% of its maximum). The time for the current to rise or fall to half its maximum is related to the inductive time constant by t = τ(ln 2) t1 τ = 2 ln2 Since the voltage across a resistor is given by V R = IR, the voltage across the resistor is established exponentially: V = V ( e t / τ 1 ) R 1 2 o Since the voltage across an inductor is given by V = L di L, the voltage across the inductor dt starts at its maximum and then decreases exponentially: V L = Ve o max ( t τ ) TP51 1999 PASCO scientific p. 153
Physics Labs with Computers, Vol. 2 Teacher s Guide P51: LR Circuit 012-06101C After a time t >> τ, a steady-state current I max is established and the voltage across the resistor is equal to the applied voltage, V o. The voltage across the inductor is zero. If, after the maximum current is established, the voltage source is turned off, the current will then decrease exponentially to zero while the voltage across the resistor does the same and the inductor again produces a back emf which decreases exponentially to zero. In summary: DC Voltage applied: I = I max 1 e ( t τ ) DC Voltage turned off: ( ) I = I max e ( t τ ) ( ) V R = V o e ( t τ ) V R = V o 1 e ( t τ ) ( ) V L = V o e ( t τ ) V L = V emf 1 e ( t τ ) At any time, Kirchhoff s Loop Rule applies: The algebraic sum of all the voltages around the series circuit is zero. In other words, the voltage across the resistor plus the voltage across the inductor will add up to the source voltage. For You To Do Use the Output feature of the ScienceWorkshop interface to provide voltage for a circuit consisting of an inductor and a resistor. (The interface produces a low frequency square wave that imitates a DC voltage being turned on and then turned off.) Use Voltage Sensors to measure the voltages across the inductor and resistor. Use ScienceWorkshop or DataStudio to record and display the voltages across the inductor and resistor as the current is established exponentially in the circuit. Use the graph display of the voltages to investigate the behavior of the inductor-resistor circuit. PART I: Computer Setup 1. Connect the ScienceWorkshop interface to the computer, turn on the interface, and turn on the computer. 2. Connect one Voltage Sensor to Analog Channel A. This sensor will be Voltage Sensor A. Connect the second Voltage Sensor to Analog Channel B. This sensor will be Voltage Sensor B. 3. Connect banana plug patch cords into the OUTPUT ports on the interface. 4. Open the document titled as shown: DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) P51 LR Circuit.DS (See end of activity) (See end of activity) The DataStudio document opens with a Graph display of voltage versus time for the Output, the resistor, and the inductor. The document also has a Workbook display. Read the instructions in the Workbook. See the pages at the end of this activity for information about modifying a ScienceWorkshop file. The Signal Generator is set to output a positive-only square wave at 3.00 volts and 50.00 Hz. The Signal Generator is set to Auto so it will start and stop automatically when you start and stop measuring data. Data recording is set to automatically stop at 0.12 seconds. POWER ScienceWorkshop 750 1 2 3 4 A B C DIGITAL CHANNELS ANALOG CHANNELS (±10V MAX INPUT) OUTPUT (±5V / 300mA) p. 154 1999 PASCO scientific TP51
PART II: Sensor Calibration and Equipment Setup You do not need to calibrate the Voltage Sensor. 1. Put the iron core into the inductor coil on the AC/DC Electronics Lab circuit board. 2. Connect a 5-inch wire lead between a component spring next to the top banana jack, and the component spring at the right hand edge of the inductor coil on the circuit board. 3. Connect the 10-ohm resistor (brown, black, black) between the component spring at the left-hand edge of the inductor coil, and the second component spring to the left of the top banana jack. 4. Connect another 5-inch wire lead between the component spring nearest to the one in which one end of the 10-ohm resistor is connected, and a component spring nearest to the bottom banana jack at the lower right corner of the circuit board. 5. Put alligator clips on the banana plugs of both Voltage Sensors. Connect the alligator clips of Voltage Sensor A to the component springs at both sides of the inductor coil. 6. Connect the alligator clips of Voltage Sensor B to the wires at both ends of the 10-Ω resistor. 7. Connect banana plug patch cords from the OUTPUT ports of the interface to the banana jacks on the AC/DC Electronics Lab circuit board. To Channel A 3 VOLT BULBS KIT NO. + A B C 3.3 Ω 3 VOLTS MAX 3 VOLTS MAX E C CW B + To Channel B To interface TP51 1999 PASCO scientific p. 155
Physics Labs with Computers, Vol. 2 Teacher s Guide P51: LR Circuit 012-06101C SAFETY REMINDER Follow all safety instructions. PART III: Data Recording 1. Use a multimeter to measure the resistance of the inductor coil on the AC/DC Electronics Lab circuit board. Record the coil resistance in the Data section. 2. Use a multimeter to measure the resistance of the 10-ohm resistor. Record the measured resistor value in the Data section. (Optional: If you have a meter that measures inductance, use it to measure the inductance of the inductor coil with the iron core inside.) 3. Begin measuring data. The Signal Generator will start automatically. Data recording will end automatically. Run #1 will appear in the Data list Analyzing the Data The voltage across the resistor is in phase with the current. The voltage is also proportional to the current (that is, V = IR). Therefore, the behavior of the current is studied indirectly by studying the behavior of the voltage across the resistor (measured on Channel B). 1. Use the built-in analysis tools in the Graph display to determine the time to half-max voltage. In DataStudio, use the Smart Tool. In ScienceWorkshop, use the Smart Cursor. Move the cursor to the top of the exponential part of the curve where the plot of voltage across the resistor (Channel B) is at its maximum. Record the peak voltage (Y-coordinate) and the time (X-coordinate) for that point in the Data table. Determine the voltage that is half of the peak (the half-max voltage). Move the cursor down the exponential part of the plot of resistor voltage until you reach the half-maximum (peak) voltage. Record the X-coordinate (time) for this point. Subtract the time for the peak voltage from the time for the half-max voltage to get the time for the voltage to reach half-max. Record this time in the Data table. 2. Calculate the inductive time constant based on the total resistance in the circuit and the value for the inductance of the inductor coil with the iron core: L = 18.9 millihenry or 0.0189 H. NOTE: If you have a meter that measures inductance, use your measured value for the inductance of the coil plus core. Inductive time constant, τ = L R. 3. Record the calculated value for the inductive time constant in the Data section. Put your results in the Lab Report section p. 156 1999 PASCO scientific TP51
Lab Report- Activity P51: LR Circuit What Do You Think? What is the relationship between the voltage across the inductor and the voltage across the resistor in an inductor-resistor circuit? What is the relationship between the current through the inductor and the behavior of an inductor in a DC circuit? Answers will vary. Data L = 18.9 millihenry or 0.0189 H for the coil plus core, unless measured otherwise. Questions Item Inductor resistance Resistor resistance Total resistance Peak voltage (for resistor) Time at peak voltage Time at half-maximum voltage Value 7.6 Ω 13.1 Ω 20.7 Ω 0.354 V 0.0086 s 0.0093 s Time to reach half-maximum 0.0007s t 12 0.0010 s τ = ln2 τ = L/R 0.0009 s 1. How does the inductive time constant found in this experiment compare to the theoretical value given by τ = L/R? (Remember that R is the total resistance of the circuit and therefore must include the resistance of the coil as well as the resistance of the resistor.) Answers will vary. For the sample data, the percent difference is 11%. 2. Does Kirchhoff s Loop Rule hold at all times? Use the graphs to check it for at least three different times: Does the sum of the voltages across the resistor and the inductor equal the source voltage at any given time? Krchhoff s Loop Rule holds reasonably well. The sum of voltages across the resistor and the inductor are somewhat difficult to measure using the Smart Cursor on the graph because the movement of the mouse by the width of one pixel changes the voltage value significantly. TP51 1999 PASCO scientific p. 157
Appendix: Modify a ScienceWorkshop File Modify an existing ScienceWorkshop file. Open the ScienceWorkshop File Open the file titled as shown: ScienceWorkshop (Mac) P44 LR Circuit ScienceWorkshop (Win) P44_LRCI.SWS This activity uses the Output feature of the ScienceWorkshop 750 interface to provide the output voltage. Remove the Power Amplifier in the Experiment Setup window. Remove the Power Amplifier Icon In the Experiment Setup window, click the Power Amplifier icon and press <delete> on the keyboard. Result: A warning window opens. Click OK to return to the setup window. Modify the Signal Generator Window Change the Signal Generator window so the Amplitude is 3.00 volts and the AC waveform is Positive-only Square Wave. Change the Sampling Options Open the Sampling Options window. Remove the Start condition. Change the Stop condition to 0.12 s. TP51 1999 PASCO scientific p. 159
Time Estimates Preparation: 15 min Activity: 30 min Objectives Students will be able to use the Output feature of the ScienceWorkshop interface to supply the voltage (positive only square wave) for a resistor-inductor circuit use Voltage Sensors to measure the voltage across the resistor and across the inductor use the Graph display to determine the time for the resistor to reach one-half of its maximum voltage calculate the inductive time constant based on the time to half-max compare the measured inductive time constant to the theoretical value Notes 1. Remember that the time scale for the graph is accurate to 0.1 milliseconds. The fifth digit to the right of the decimal on the horizontal axis is uncertain. 2. One way to measure voltages for a specific time for both the inductor and resistor is to use the Graph display. A second way is to examine the individual data points in a Table display. Open a Table display. Click the Time button ( voltage and the corresponding time. DataStudio Sample Data ) to view both the value of TP51 1999 PASCO scientific p. 161
Physics Labs with Computers, Vol. 2 Teacher s Guide P51: LR Circuit 012-06101C p. 162 1999 PASCO scientific TP51